Libertine FPE Technology Brief: Bounce chambers for Linear Generators

Linear Generators are a new category of power generator that offer the efficiency of fuel cells with the cost and durability of conventional internal combustion (IC) engines, ultra-low engine-out emissions, and the flexibility to use a wide range of renewable fuels. Clean power from renewable fuels can complement intermittent renewables on the grid and complement battery electrification in transport, accelerating the pace of decarbonisation and powertrain electrification.??

Libertine has been developing Linear Generator platform technology on customer-led programmes for over a decade. Since 2020 we have been working to develop our next generation intelliGEN LGN60-P1 performance validation prototype through motored operation and combustion testing, and in 2022 we began a collaboration with Ashok Leyland working towards vehicle integration and demonstration in their commercial vehicle portfolio.

Libertine’s LGN60-P1 performance validation prototype is an opposed free piston Linear Generator created using Libertine’s intelliGEN IGN60 platform. More specifically, it is an opposed free piston, direct injection, uniflow scavenged two-stroke Linear Generator product combining Libertine’s linear motor-generators, power electronics and piston motion control systems. Its modular construction allows for single and multi-cylinder configurations for a range of outputs from 60-160kWe. With a little over 2.5 litres of trapped volume per cylinder, LGN60-P1 is considerably larger and more powerful than Libertine’s ‘IGN20-MVP’ proof of concept engine that was tested with MAHLE Powertrain in 2020.

Following completion of a first phase of combustion testing with MAHLE Powertrain earlier in 2023 we are now implementing further enhancements for performance and durability, and building several single cylinder systems with these enhancements for use in test cell development within client programmes from 2024Q1.

In this technology brief we describe the role of bounce chambers within opposed free piston systems, and how these contribute to Linear Generator efficiency and power density.

Linear Generators 101

One of the most common questions we get when describing how an opposed free piston Linear Generator works is ‘How do the movers return to the centre of the machine at the end of the power stroke?’. In theory this could be done by using the linear electrical machines as motors, but this approach has two fundamental problems.

Firstly, linear electrical machine (LEM) efficiency falls off with speed: The slower the motion, the less efficient the motoring (or generating) power conversion. This is because LEM electrical power losses are approximately proportional to the square of the electromagnetic force applied, whereas the useful motoring (or generating) work rate is equivalent to the electromagnetic force multiplied by the velocity – Hence to turn the pistons around at ‘Bottom Dead Centre’ the LEM would need to produce a large force at the end of the power stroke, where the velocity falls to zero, which would be an inefficient waste of the precious electrical power we’re aiming to generate as useful output.?

Secondly, to bring the movers to rest at the end of the power stroke using only the LEMs, all the energy added by the fuel and air in the power stroke would need to be converted to electrical energy in that single stroke. This would require more substantial and costly linear electrical machines compared those required for a more leisurely pace of energy recovery over the course of both strokes in a complete cycle.

But to do this, some of the energy added in the power stroke needs to be stored up and returned to power the compression stroke. The question is, how to store this energy?

Short stroke free piston Stirling engines (which use gas compression and expansion in a closed cycle to convert heat to electrical power) often use a mechanical spring or ‘flexure’ as a small energy store for this purpose. With longer stroke free piston machines, a mechanical spring is also possible but so far such efforts have been thwarted by the inherent material fatigue failure risks that plague mechanical springs (and litter the highways with the broken ends of suspension coil springs)

When I began my career making race engines in the Indycar department at Cosworth in Northampton, regulations prevented us from using the air valves that allowed our F1 colleagues to make their engines rev to 20,000 rpm or more. Fortunately, when it comes to Linear Generators, there’s no such rule book, and the bounce chambers we employ to store a proportion of the power stroke energy and then return this during the compression stroke are essentially beefed up versions of F1 air valves.

To see how these bounce chambers help to smooth out the generation of electrical power across both the power stroke and the compression stroke, the energy ‘waterfall’ chart below illustrates the system energy flows and balances through a complete cycle (ignoring for a moment the inevitable mechanical losses) from the perspective of a single ‘LEM + bounce chamber’ or Linear Electro-Mechanical System (LEMS) forming one half of the opposed free piston system within a Linear Generator.

Starting from the left of the chart, at TDC (‘Top Dead Centre’ refers the point when the pistons are closest together at the beginning of the power stroke), the main chamber contains compressed gas and some fuel that is in the process of reacting with the air. In the first bar, the red block indicates the ‘expansion work potential’ that will be added by the fuel, once fully reacted. The smaller blue block represents the ‘work of compression’ that has been invested in the compression stroke to achieve the conditions for efficient, clean combustion (don’t worry, we’ll get that back later).

In the first part of the power stroke, the energy from air and fuel at TDC powers the acceleration of the mover, and by mid stroke (the second bar) much of this is now in the form of kinetic energy. The chart shows some of the expansion work potential still there at mid stroke, as the gas in the main working chamber has not yet full expanded. There is also an amount of energy already stored in the bounce chamber whose contents are now being compressed. The total energy in the system at mid stroke is a bit less than at TDC, as some of the energy has been recovered by the LEM, acting as a generator to producing useful electrical power output.

What happens next very much depends on the function and performance of the bounce chamber, as the mover’s kinetic energy (and the working chamber gas that continues to power it towards the end of stroke) is at this point way more than has been recovered by the LEM so far. As the bounce chamber continues to compress, the energy that is stored grows rapidly so that by BDC (‘Bottom Dead Centre’, the end of the power stroke) the bounce chamber illustrated in the chart now stores all the mid-stroke kinetic energy plus the balance of the work from the now-exhausted main chamber.

As an energy store, the bounce chamber contents at BDC are sufficient to power continuing electrical energy recovery on the compression stroke, and give back the work of compression to the main chamber so that the whole cycle can start again from the next TDC.

This simplified view yields three important insights regarding the opposed free piston architecture and the role of bounce chambers:

Firstly, a bounce chamber is not going to be a perfect spring. There will be some compression & expansion losses due to friction, gas leakage and heat losses. It might be better to recover a bit more than half of the energy on the expansion stroke and avoid some of those bounce losses – but that would result in slightly more LEMS losses. So bounce chamber efficiency really matters for Linear Generator efficiency.

Secondly, the compression stroke is going to be slower than the expansion stroke. It has to be, because some of the kinetic energy present at the expansion mid stroke has been recovered by the LEMS by the time the compression stroke is underway. This slowed compression stroke lowers the frequency of the whole cycle, which in turn reduces the power output per LEMS. We could tweak the motion profile to reduce the LEMS generating force in ‘Energy recovery period 3’ and get some of this power density back, but at the cost of additional LEMS force (and losses) during ‘Energy recovery period 4’. To minimise this penalty a bounce chamber must discharge its energy quickly so that less time is spent on the turnaround and getting back up to speed. So bounce chambers need to be stiff, returning most of the stored energy in the early part of the compression stroke. ??

Thirdly, each mover is also an energy store. Through the cycle, system energy is sloshing back and forth between three energy storage reservoirs: The compression work in two gas columns of the main chamber and the bounce chamber; and the kinetic energy of the free piston mover that oscillates between them. Reducing the mass of the free piston mover provides another way to increase system frequency and output, but in turn alters the compression and expansion rates around TDC, influencing the progression of the combustion event. So the bounce chambers are part of a kinetic system that affects the efficiency of the both the LEMS and the combustion event.

These insights have informed Libertine’s approach to the design of the bounce chambers within the intelliGEN platform. To minimise heat losses, bounce chambers are tucked away deep inside the LEMS, formed within small pockets inside the pistons that face the main chamber and whose high temperature acts as an effective barrier to further heat losses from the compressed bounce chamber gas. The bounce chambers are sealed by the same non-contact gas bearings inside the translator that support the electrical machine side-loads and guide the linear motion, minimising bounce chamber friction and leakage losses. And the bounce chambers can be configured with different gas feed pressures and compression ratios to provide the desired stiffness and energy storage according to each application’s fuel and operating requirements.

intelliGEN sub-system simulation and performance development

Libertine has an array of test cells at our facilities in Sheffield where we put the intelliGEN platform sub-systems through their paces before integrating these into complete cylinder builds. This allows us to progress and validate multiple enhancements in parallel. It also allows us to capture performance data to characterise each sub-system, so that these characteristics can be integrated into a digital twin of the complete Linear Generator prototype for control performance development, well before the physical system is complete.

A digital twin is a virtual representation of a physical system used for performance development and diagnostics. It uses a detailed model created via multi-physics simulation tools and validated using empirical data to mimic the expected behaviour, performance, and characteristics of the physical system – in our case the LGN60-P1 Linear Generator prototype. Simplified versions of this model can be run in real-time and controlled using the actual intelliGEN control hardware. This approach, known as ‘Hardware in Loop’ (HIL) testing, speeds up control performance development, and significantly reduces the time, cost and risk that would be involved in an equivalent amount of physical testing.??

Although the complete IGN60-P1 Linear Generator prototype is quite complex in terms of the physics and system interactions, modelling the system kinetics is relatively straightforward as there is only one axis of motion to consider, and all the forces acting on each mover together produce the acceleration and resulting velocity in this one dimension that can be measured directly for model validation.

In Libertine’s 1D ‘Chamber-Kinetic-Control’ (CKC) model framework illustrated above the ‘Inertial Term Force Function’ is the sum of all the forces applied by the piston, the bounce chamber, the bearing system and the electrical machine translator, which together cause the mover to accelerate.

Note that in our terminology, a mover (short for ‘Free Piston Mover’) is the combination of a piston (facing the main working chamber) and an electrical machine translator, usually formed using a magnet array, that interacts with the stator to generate power.

The CKC framework is at the heart of our approach to sub-system development and performance validation, and provides the means for our customers to incorporate and evaluate the system impact of their own working chamber modelling and application control algorithms (highlighted in yellow in the figure above).

The sharp-eyed will notice that the CKC framework also includes a ‘Residual Term’. This can account for any variance between the expected performance from simulation, and the measured empirical performance. More than just a plug, this term provides the basis for variance analysis and model fitting in development, and for diagnostics and predictive maintenance in production.

The CKC framework can also produce discrete loss components associated with each of the constituent blocks, and so provides the means to estimate system efficiency and identify opportunities for efficiency gains via the co-optimisation of combustion calibration, LEMS design and motion control.

Bounce chamber testing

We run our bounce chamber testing on a ‘half-engine’ test set-up: A single LEMS, plus a main working chamber that contains a volume of air that can be compressed and expanded to produce forces equivalent to those in the internal combustion system of the complete IGN60 Linear Generator. This is easier said than done, as the forces are substantial. Motoring the main chamber with a compression ratio of around 18:1, a typical operating point for our hydrous bioethanol test fuel, produces peak pressures in the region of 45 bar (4.5MPa) and a total force of over four tonnes. For this reason, the half engine is run vertically so that the main chamber force points directly down onto a fixed bed plate. The bounce chamber pressure acts over a smaller area but even at a relatively modest 20 bar (2MPa) peak pressure this generates nearly a tonne of upward pressure force. At a peak pressure of 50 bar (5MPa), the bounce chamber force would be sufficient to lift the entire half-engine, mounting frame and bed plate clean off the ground. Not bad for a tiny pocket of gas about the size of a coffee cup.

It’s worth bearing in mind that when two of these are bolted together to form a complete cylinder, we are entirely reliant on the precision of our motion control to ensure that the simultaneous and opposing bounce forces acting at each end of the machine cancel out, about twenty times every second (20Hz).

To give ourselves some additional headroom, we added 1.2 tonnes of concrete blocks.

A typical test involves switching on the gas bearings, activating the bounce chamber feed, and then using the LEMS to motor a small number of test cycles (typically 50-100) from which we can calculate average cycle data and derive the bounce chamber efficiency and stiffness at each target operating point.

In the plot from the test illustrated above, the area beneath the blue pressure trace represents the average energy stored in the bounce chamber and returned during the compression stroke of each cycle during the test. The area contained within the blue loop (Look closely, there are two lines forming a thin loop) represents the average bounce chamber energy loss per cycle due to pressure leakage and heat loss.

So, what’s next?

In this technology brief we’ve looked at the role of bounce chambers within opposed free piston systems, how these contribute to Linear Generator efficiency and power density, and how Libertine simulates, develops and evaluates bounce chamber system performance.

In the coming weeks we’ll be evaluating? further sub-system enhancements to our encoder systems, bearings and motion control platform so that once our enhanced LGN60 cylinders come together we can be confident in their efficiency, power output, control and durability performance ready for the next phase of combustion testing.